Development of ACERA Learning Model Based on Proof Construction Analysis

Abstract

Proof constructing is the process of justifying a claim using the methods and concepts of proof to produce mathematical proof. Proof constructing is also an aspect of proof, and is often the only way to assess student performance. However, proof construction is still a constant problem (difficulty) for every student. The cause of this difficulty is not only because of the content of proof in textbooks/sources, over-reliance on examples, understanding, underlying logic, and the ability to use proof writing strategies, but also due to the lack of proof discussion activities that train students to understand and answer proof practice questions, give proof reasoning against the proof that has been constructed, and validating own and other colleagues' answers. Thus, this study aims to develop a valid and practical ACERA (Activities, Classroom Discussion, Exercises, Reason, and Audience) learning model and has a potential effect on students' ability to proof construction. This study uses research design research development methods in three stages, namely the preliminary stage, the model development stage and the assessment stage. The research subjects were 23 students of the Mathematics Education study program at the University of Mataram. The development of the ACERA model offers an alternative solution to reduce the difficulty of proof construction, thus enabling this model to have characteristics that are valid, practical and have a potential effect in increasing the productivity of student proof construction.

Keywords

• proof construction
• activities
• classroom discussion
• exercises
• reason
• audience.